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Few charges exist in 3-D space. The potential due to the system of charges at an origin depends on:

A. The magnitude of each charge.

B. The distance of each charge from point P. 

C. The angles between the position vector of each charge make with the x, y, and z axes. 


1. Only A and some constants
2. Only A, B and some constants
3. ​A, B and C and some constants
4. independent of all the above quantities

1 Answer

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Best answer
Correct Answer - Option 2 : Only A, B and some constants

CONCEPT:

  • Electric potential is equal to the amount of work done per unit charge by an external force to move the charge q from infinity to a specific point in an electric field.

\(⇒ V=\frac{W}{q}\)

  • Potential due to a single charged particle Q at a distance r from it is given by:

\(⇒ V=\frac{Q}{4\piϵ_{0}r}\)

Where, 

ϵ0 is the permittivity of free space and has a value of 8.85 × 10-12 F/m in SI units

  • Potential at a point P due to a system of charged particles Q1, Q2, Q3, ... Qn having distances r1, r2, r3, ... rn respectively from point P is given by:

\(⇒ V=\frac{Q_1}{4\piϵ_{0}r} + \frac{Q_2}{4\piϵ_{0}r} + \frac{Q_3}{4\piϵ_{0}r} + ...+\frac{Q_n}{4\piϵ_{0}r}\)

\(⇒ V=\sum_{i=1}^{n}\frac{Q_i}{4\piϵ_{0}r_i}\)

EXPLANATION:

  • Since potential at a point P due to a system of charged particles is given by:

\(⇒ V=\sum_{i=1}^{n}\frac{Q_i}{4\piϵ_{0}r_i}\)

  • The potential depends on all of the following three quantities
  1. The magnitude of each charge.
  2. The distance of each charge from point P.
  3. The permittivity of the medium in which the charges and P exist.
  • Therefore option 2 is correct.

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